Genady

I think that infinite set is an object that exists in mathematics in the same sense as 3. I don't think that (0,1) is said to end.

For example, does a number 3 exist? Does an open interval (0,1) end?

Isn't it already established in a variety of ways that they don't solve problems?

Yes, this is a procedure. What is a resulting pattern?

I see an ambiguity in the question 1 in the concept of "exist." And an ambiguity in the question 2 in the concept of "end." Answers to both questions depend on interpretation of these terms more, or rather than on interpretation of the term "infinity."

You have a rope and a lighter. If you light a rope, it burns about 1 m in 1 hour. However, it does not burn at a uniform rate, e.g., not necessarily 0.5 m in 0.5 hour. Can you measure 0.5 hour? 15 minutes? 20 minutes?

Yep.

There might be. For simplicity, and according to the fact that English is the current language of science communication, I'd limit the discussion to English.

(Inspired by the @mistermack's post above.) ChatGPT could not make the logical step to figure out the following question (and evidently is not familiar with the Chinatown movie) Me: Katherine is Evelyn's sister and daughter. Explain. ChatGPT: It seems there is a contradiction in your statement. If Katherine is both Evelyn's sister and daughter, it implies an inconsistency in the family structure. In traditional family relationships, a sister and a daughter are two distinct roles within a family. Let's examine the possibilities separately: If Katherine is Evelyn's sister: This means Katherine and Evelyn share at least one parent, typically their mother or father. They are siblings and have a common parentage. If Katherine is Evelyn's daughter: This implies that Evelyn is Katherine's mother. In this scenario, Evelyn is the parent, and Katherine is the child. Based on the given information, it is not possible for Katherine to be both Evelyn's sister and daughter. If there is additional context or clarification, please provide it so that I can better assist you.

ChatGPT has handled it very well: In the given scenario, there are two individuals: an Englishman and an American. Let's refer to them as John (the Englishman) and Mark (the American). "The Englishman is the father of the American's son" means that John is the biological father of Mark's child. To further explain the situation, we need to consider a few possibilities: John and Mark are in a same-sex relationship: In this case, they may have used a sperm donor or a surrogate to have a child together. As an Englishman, John would be the biological father, and the child would be their son. John had a previous relationship with a woman and fathered a child: Before being in a relationship with Mark, John might have been in a heterosexual relationship and had a child. Later, he entered a relationship with Mark, who became the child's stepfather or co-parent. Adoption or surrogacy: John and Mark may have adopted a child together or opted for surrogacy, where John is the biological father, and Mark is the legal father. These are just a few possible explanations to illustrate how the Englishman could be the father of the American's son. The specific circumstances would depend on the individuals involved and their personal situation.

AFAIK, Riemann surfaces are not related to the Riemann hypothesis. Greeks were fascinated with numbers philosophically. As opposed to Romans, who built cities. As for the other questions, I'd like to know the answers, too.

Why not? In fact, the original version of the puzzle was a multiple-choice, and the choices were: I.e., originally, "Teresa's daughter" was the only correct answer.

Yes, of course.

What they can do is given. 5 ly in the planetary systems FoR.

The numbers I find are: 38 000 mph for Voyager 1, 196 000 mph for Oumuamua. What are your numbers?

A tribe of nomadic aliens is located in a planetary system that can supply them with sufficient resources to get to the next resource rich system. The next such system is 8 ly away, and there is only empty space in between. They can carry enough resources, a "load", to go 5 ly. They can make storages of any size on the way. What is the minimum amount of loads they will need to get to the next system? Is there a limit to the distance between systems that they can cross?

Oh, I see now what you mean. No, I don't think they would be interested to drop in and visit their "mines", i.e., planets. And I don't think that any aliens have been sighted on Earth. They would rather use robots. Like we do.

This was fun. Same to you.

A being adapted to low-g would have difficulty existing in higher-g environments. For a being adapted to much higher than 1 g, they might not have developed space travel at all, owing to the energy required to lift payloads into space. I was talking about evolution that occurs during the nomadic lifestyle.

And if they maintained this lifestyle for several thousand years, they might biologically evolve to better fit it, e.g., no need for gravity, radiation tolerance, boredom tolerance, etc.

I don't think it was a possibility, technically, financially, and logistically. Too fast, too short, too far, too late, too expensive ...

How obvious is that? Picking on Plastics | Smithsonian Science Education Center (si.edu)

Perhaps the "low metabolism" idea was bad. Let's drop it. The "nomadic aliens" idea still stands.

There are many kinds of Riemann stuff, pretty much everywhere in math. This specific stuff directly relates to Riemann geometry, and I don't know of a connection between this and prime numbers.